Sondipon Adhikari Anjan Dutta Satyabrata Choudhury Editors ...

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Lecture Notes in Civil Engineering Sondipon Adhikari Anjan Dutta Satyabrata Choudhury   Editors Advances in Structural Technologies Select Proceedings of CoAST 2019

Transcript of Sondipon Adhikari Anjan Dutta Satyabrata Choudhury Editors ...

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Lecture Notes in Civil Engineering

Sondipon AdhikariAnjan DuttaSatyabrata Choudhury   Editors

Advances in Structural TechnologiesSelect Proceedings of CoAST 2019

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Lecture Notes in Civil Engineering

Volume 81

Series Editors

Marco di Prisco, Politecnico di Milano, Milano, Italy

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Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup,WA, Australia

Anuj Sharma, Iowa State University, Ames, IA, USA

Nagesh Kumar, Department of Civil Engineering, Indian Institute of ScienceBangalore, Bengaluru, Karnataka, India

Chien Ming Wang, School of Civil Engineering, The University of Queensland,Brisbane, QLD, Australia

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Lecture Notes in Civil Engineering (LNCE) publishes the latest developments inCivil Engineering—quickly, informally and in top quality. Though originalresearch reported in proceedings and post-proceedings represents the core ofLNCE, edited volumes of exceptionally high quality and interest may also beconsidered for publication. Volumes published in LNCE embrace all aspects andsubfields of, as well as new challenges in, Civil Engineering. Topics in the seriesinclude:

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Sondipon Adhikari • Anjan Dutta •

Satyabrata ChoudhuryEditors

Advances in StructuralTechnologiesSelect Proceedings of CoAST 2019

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EditorsSondipon AdhikariSwansea UniversityWales, UK

Satyabrata ChoudhuryNational Institute of Technology SilcharSilchar, Assam, India

Anjan DuttaIndian Institute of Technology GuwahatiGuwahati, Assam, India

ISSN 2366-2557 ISSN 2366-2565 (electronic)Lecture Notes in Civil EngineeringISBN 978-981-15-5234-2 ISBN 978-981-15-5235-9 (eBook)https://doi.org/10.1007/978-981-15-5235-9

© Springer Nature Singapore Pte Ltd. 2021This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,Singapore

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Preface

National Conference on Advances in Structural Technologies (CoAST-2019) heldduring 1–3 February, 2019, was aimed towards a national level forum for profounddiscussions with shared interest on novel research and developments in the entiredomain of structural engineering. Academicians, researchers, consultants, practic-ing engineers working in government/private sectors from all over India weresincerely encouraged to participate in this national conference. CoAST-2019 wasalso a good opportunity for many to visit the North-Eastern part of India.

Wide ranges of topics/themes associated with Structural Engineering wereconsidered in CoAST-2019, like: Solid Mechanics, Computational Mechanics andModelling, Composite Structures, Emerging Structural Materials, Structural HealthMonitoring, Vibration Control, Probabilistic Structural Mechanics, etc. Most of thetopics have been represented in the selected papers.

CoAST-2019 was the first national level conference in the domain of StructuralEngineering organized by National Institute of Technology (NIT) Silchar. NITSilchar, an Institute of National Importance under the NIT Act, was established in1967, as Regional Engineering College (REC) Silchar, in Assam. In year 2004, itwas upgraded to the status of an NIT.

I am thankful to Prof. Sivaji Bandyopadhyay, Director, NIT Silchar andProf. Parthasarathi Choudhury, Head, Civil Engineering Department, NIT Silchar,for their encouragement in various steps of the Conference. It is thankfullyacknowledged that the Conference was funded by TEQIP-III.

We are thankful to the following keynote speakers: Prof. Biswajit Bhattacharjee(IIT Delhi), Prof. Nirjhar Dhang (IIT Kharagpur), Prof. Siddhartha Ghosh (IITBombay), Prof. Balaji Raghavan (INSA, Rennes, France), Dr. Debiprasad Ghosh(DGM, L&T).

I wish to convey thanks to my colleagues, some of whom I mention here:Prof. A. I. Laskar, Dr. Nirmalendu Debnath, Dr. B. K. Roy, Dr. Arjun Sil, PallabDas, Dr. Subhrajit Dutta, Dr. M. L. V. Prasad Raju, Dr. Debjit Bhowmick,Dr. Sudip Dey, Dr. Nitsh A. and others.

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Such a big event could not have been organized without the help of our studentsforce. I wish to mention the names of research scholars like, Sourav Das, DurgaMibang, Kamalesh Bhowmick, Subham Ghosh, Mrinal Kanti Sen, Sandeep Das,Pritam Hait, especially. And last but not the least, the contributions of our PGstudents: some names which I remember are: Navendu Nimare, Suman Banerjee,Anneta A. Joseph, Sitesh Mohapatra, Charla Venkatesh, Bharti Mishal, MayuriBorah, Nazeel Sabha, Sudipta Malakar, etc.

We are thankful to Springer Publications for their consent in publishing aSCOPUS indexed proceedings of the selected papers of CoAST-2019. Springer hasnot only added extra flavour to the conference, but also encouraged contributors ofpapers.

I am thankful to Prof. Sondipon Adhikari, Swansea University and Prof. AnjanDutta, IIT Guwahati for their editorial works and guidance. Thanks due to ourreviewers and finally to our participants who made the conference a success.

Hope this proceedings will throw new light to the researchers and motivate themfurther in research.

Satyabrata ChoudhuryChairman CoAST-2019

Professor in Civil EngineeringNIT Silchar

Silchar, India

vi Preface

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Contents

Seismic Control and Performance of Passive Hybrid Damper UnderNear-Field Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Swabarna Roy, Swagato Das, and Purnachandra Saha

Wall Effects on Terminal Velocity of Test Fuel Bundle in the Fuel TestLoop of High Flux Research Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 15G. Verma, S. Sengupta, S. Mammen, P. Mukherjee, and P. V. Varde

Comparison of Seismic Performance of Composite (RCS) Framewith RC Frame Using Pushover Analysis . . . . . . . . . . . . . . . . . . . . . . . . 31Manoranjan Singh Oinam and S. S. Ningthoukhongjam

Investigating Load Withstand by L-Shape Concrete Cube, RCC Slaband to Safeguard Reinforcement of RCC Slab in SaltwaterEnvironment Using Cathodic Protection . . . . . . . . . . . . . . . . . . . . . . . . 45C. F. Rajemahadik, M. M. Kulkarni, R. S. Durge, A. R. Kamble,S. B. Babar, and P. A. Bansode

Performance Evaluation of Two-Way RC Slab Subjected to BlastLoading Using Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 57Kasturi Bhuyan, Kiran Kumar Jujjavarapu, and Hrishikesh Sharma

Development of Fragility Curves for Different Types of RCFrame Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Neeva Ahanthem and S. S. Ningthoukhongjam

Smart Lightweight MR Damper for the Enhancementof Seismic Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89C. Daniel, G. Hemalatha, L. Sarala, D. Tensing, and S. Sundar Manoharan

Rheological Behavior of Geopolymer Mortar with Fly Ash, Slagand Their Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Biswajit Roy and Aminul Islam Laskar

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Effect of Pile Spacing and Raft Thickness on the Behaviourof Piled-Raft Foundation—A Parametric Study Using FEM . . . . . . . . . 111Mukul Kalita, Utpal Kumar Nath, and Palash Jyoti Hazarika

Removal of VOCs and Improvement of Indoor Air QualityUsing Activated Carbon Air Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Sujon Mondal, Soham De, and Purnachandra Saha

A Comparative Study of Normal and Self-compacting Concrete . . . . . . 133Deep Tripathi, Rakesh Kumar, P. K. Mehta, and Amrendra Singh

Evaluating Toughness as a Parameter to Determine the Fatigue Lifeof Wollastonite Microfiber Reinforced High Flow PavementQuality Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Shashi Kant Sharma and K. P. Marisarla Chaitanya

Response of Single and Multilayered Flexible Base for Staticand Earthquake Loading Under Framed RC Structure . . . . . . . . . . . . . 169Gaurav D. Dhadse, G. D. Ramtekkar, and Govardhan Bhat

Analysis of Moment and Torsion in Skew Plates Using ABAQUS . . . . . 185Anjani Kumar Shukla, Vishal Koruthu Philip, and P. R. Maiti

Behavior of Liquid Storage Tank Under MultidirectionalExcitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Sourabh Vern, Mahendra Kumar Shrimali, Shiv Dayal Bharti,and Tushar Kanti Datta

Osdag: A Software for Structural Steel Design Using IS 800:2007 . . . . . 219Siddhartha Ghosh, Danish Ansari, Ajmal Babu Mahasrankintakam,Dharma Teja Nuli, Reshma Konjari, M. Swathi, and Subhrajit Dutta

Experimental and Analytical Investigations on Two-Way FlexuralCapacity of Biaxial Voided Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233R. Sagadevan and B. N. Rao

A Comparative Study of Seismic Response of Structure Isolatedwith Triple Friction Pendulum Bearing and Single Friction PendulumBearing Under Different Hazard Levels of Earthquake . . . . . . . . . . . . . 249Ankit Sodha, Sandip Vasanwala, Devesh Soni, and Shailendra Kumar

Assessment of Important Parameters for Seismic Analysis and Designof Confined Masonry Buildings: A Review . . . . . . . . . . . . . . . . . . . . . . . 261Bonisha Borah, Vaibhav Singhal, and Hemant B. Kaushik

Design and Performance Criteria for Fire-Resistant Designof Structures––An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277Nitant Upasani, Mansi Bansal, Ashirbad Satapathy, Sanket Rawat,and G. Muthukumar

viii Contents

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Wear Behavior of Marble Dust Filled Aluminum Metal MatrixStructural Composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Hariom Tripathi and Sandeep Kashyap

Quantifying Uncertainty in Structural Responses of PolymerSandwich Composites: A Comparative Analysis of Neural Networks . . . 305R. R. Kumar, T. Mukhopadhyay, K. M. Pandey, and S. Dey

Buckling Analysis of Braced Frames under Axial and LateralLoadings: The Effect of Bracing Location . . . . . . . . . . . . . . . . . . . . . . . 317Narayan and Krishna Kant Pathak

A Study on Moment–Curvature Relationships for REINFORCEDCONCRETE BEAMS with Varying Fire Loading Conditions . . . . . . . . 335Ankit Borgohain and Sriman Kumar Bhattacharyya

Effect of Slab Thickness on Period of the Vibration of ReinforcedConcrete Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353Prabhat Kumar Soni, S. K. Dubey, and Prakash Sangamnerkar

Sampling-Based Techniques for Finite Element Model Updatingin Bayesian Framework Using Commercial Software . . . . . . . . . . . . . . . 363Ayan Das and Nirmalendu Debnath

Stochastic Structural Optimization of Multiple Tuned Mass Damper(MTMD) System with Uncertain Bounded Parameters . . . . . . . . . . . . . 381Kamalesh Bhowmik and Nirmalendu Debnath

Hearth Monitoring of Blast Furnace Using Finite Element Analysisand Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393Debi Prasad Ghosh, Bhaskar Sengupta, and Shyam Krishna Maitra

Fatigue Resistance of Recycled Steel Fibers (Discarded Vehicle TyreSteel Fibers) Concrete Pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407M. V. Mohod and K. N. Kadam

Contents ix

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About the Editors

Prof. Sondipon Adhikari is the chair of Aerospace Engineering in the College ofEngineering of Swansea University (from April 2007) and a Fellow of the RoyalAeronautical Society (from April 2017). In 2010 he received the Wolfson ResearchMerit Award from the Royal Society (UK academy of sciences). He was anEngineering and Physical Science Research Council (EPSRC) Advanced ResearchFellow (2004-09) and winner of the Philip Leverhulme Prize (2007) in Engineering(given to an outstanding scholar under the age of 35). He received his Ph.D. in 2001as a Jawaharlal Nehru Memorial Trust scholar at the Trinity College from theUniversity of Cambridge. He was a lecturer at the Bristol University (2003–07) anda Junior Research Fellow at Fitzwilliam College, Cambridge (2001–03). From2015, he has been a Distinguished Visiting Professor at the University ofJohannesburg. He was a visiting Professor at Carleton University (Canada, 2006)and a visiting scientist at the Los Alamos National Laboratory (USA, 2006). In2008, he was an official visitor to the Cambridge University EngineeringDepartment and a visiting Fellow of Fitzwilliam College, Cambridge. In January2016, he was a visiting Professor at the University of Paris East.

Professor Adhikari’s research stands on three fundamental footings - structuraldynamics, probabilistic methods and computational mechanics. Specific researchareas include uncertainty quantification in computational mechanics, dynamics ofcomplex systems, inverse problems for linear and non-linear dynamics, vibrationenergy harvesting, wind turbines and dynamics of nanoscale systems. He hasobtained more than £2.5M of competitive research funding as a principal investi-gator, published 5 books, 286 peer-reviewed journal papers (Scopus h-index = 51)and more than 185 conference papers in these areas. He was the recipient of theJawaharlal Nehru Memorial Trust (London) scholarship at the Trinity College,Cambridge (1997). In 1999, he had won the best student paper prize (John WinboltPrize) from the Cambridge University, for a single-authored paper in the AIAAJournal. In 2001, he had won the second prize from the Acoustical Society ofAmerica, for the best student paper/presentation in the 141st Meeting in Chicago.Later that year he received the junior research fellowship (in science and engi-neering) from Fitzwilliam College, Cambridge. Professor Adhikari received the

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EPSRC advanced research fellowship award in 2004. He was a member of thewinning project team in the EPSRC Ideas factory Workshop (January 2006) onScientific Uncertainty and Decision-Making (awarded £338,591). Prof. Adhikarihad won three highly competitive Newton Fellowships, two Marie CurieInternational Fellowships and the Newton-Bhabha award.

Prof. Adhakari has been an Associate Editor for the Shock and Vibration Journalbetween 2006–2011. He is a technical reviewer for over 120 international journals,20 conferences and 15 funding bodies. He is a member of the American Institute ofAeronautics and Astronautics (AIAA) Nondeterministic Approaches TechnicalCommittee (NDA-TC) and Uncertainty Quantification and Model Validation(UQMV) technical division of the Society for Experimental Mechanics (SEM).Professor Adhikari is a member of the Engineering and Physical Sciences ResearchCouncil (EPSRC) peer-review college. He has been a research grant reviewer forNuffield foundation, NRF (National Research Foundation), South Africa, USDepartment of Energy and Science and Technology, book reviewer for Wiley,Elsevier/Butterworth-Heinemann Publishers and Royal Aeronautical Society.

Prof. Anjan Dutta is HAG Professor in the Department of Civil Engineering, IITGuwahati, India. He had his Bachelor degree from REC Silchar, Master’s degree inStructural Engg from IIT Madras and Ph.D. from IIT Delhi. He worked as Lecturerat REC Silchar, as assistant professor and associate professor at IIT Guwahati, andis presently a professor in the same institute.

He has 59 publications in international referred journals, many papers in inter-national and national conferences. His research interests are: Finite Elementmethod, Bridge Engineering, Optimization, Structural Control, Health Monitoring,Structural Retrofitting. He was a Gold medalist of Gauhati University (B.E.),received Commendation certificate from IRC and was felicitated as EminentEngineer by Institute of Engineers (India). He has a patent on “Elastomeric SeismicIsolation with High Damping Capacity and Manufacturing Method Thereof”. Basedon this patent philosophy, a two-storey Masonry building supported on isolators hasbeen constructed in Tawang, Arunachal Pradesh, India. This is the first prototypebuilding in the world on Fibre Reinforced Elastomeric Isolators. He has guided 11Ph.D. scholars, and is currently supervising another half a dozen scholars. He hascompleted 9 sponsored research projects. He has published one book chapter. Prof.Dutta has contributed a large number of consultancy services to many prestigiousprojects. He is member of various committees and has rendered services to IITGuwahati, in various capacities like Dean (Institute Works), Head of theDepartment, etc.

Prof. Satyabrata Choudhury is working as a Professor in the Department of CivilEngineering, NIT Silchar, India. He has been a faculty of this institute since 1983,first as Lecturer and then as Assistant Professor, and now as Professor. Prof.Choudhury obtained his bachelor's degree in Civil Engineering from REC Silchar(Now NIT Silchar), India. He obtained his master’s degree in StructuralEngineering from IIT Kharagpur, and Ph.D. in Earthquake Engineering from IIT

xii About the Editors

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Roorkee. He has served in various administrative positions in the institute includ-ing: Head of the Department, Dean (P&D), Coordinator of various activities.

He has received various awards including President of India’s prize, Dr. JaiKrishna Gold medal (two times), Institution prize (IEI), etc.

His area of research is Performance-based seismic design. He has 17 papers ininternational peer reviewed journals, 6 papers in national journal and number ofpapers in international and national conferences. He has supervised about 50 M.Tech. dissertations, produced two Ph.D. and working with another 10 Ph.D.scholars. He has evolved a new design methodology named as Unifiedperformance-based design (UPBD) which accommodates both drift and perfor-mance level as target design objectives. This method also provides member sizes.

About the Editors xiii

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Seismic Control and Performanceof Passive Hybrid Damper UnderNear-Field Earthquakes

Swabarna Roy, Swagato Das, and Purnachandra Saha

Abstract In structural engineering aspect, the inherent structural property of thebuilding is not sufficient to control the structural response when it comes to strongearthquakes. The common control strategy used by researchers makes use of energydissipating devices that absorb the energy imparted to the structure due to earth-quake and dissipate the energy by their hysteresis nature. In this study, seismicresponse of a G + 4 storey building installed with a hybrid damper has been inves-tigated. The hybrid damper system comprises of Viscous Fluid Damper (VFD) andShape Memory Alloy (SMA). The performance of the building under near-fieldearthquakes, Tabas, Kobe, and Gebze earthquakes has been evaluated. The dampershave been installed at the base of the superstructure. SMA exhibits a good self-centering capability and is known for its superior super-elasticity properties. It iscapable of dissipating energy through its hysteresis nature while maintaining a lowlevel of residual displacement. VFD dissipates energy through the movement of fluidinside it, which minimizes both stress and displacement the structure due to seismiceffect. The time history analysis result shows the effectiveness of hybrid damper forcontrolling the seismic forces acting on the structure. In this present study, there is asignificant reduction in base shear and displacement by about 16% and 8% by usingHybrid damper when compared to VFD and SMA dampers. A comparative study ismade showing the effect of the Hybrid damper in reducing the seismic responses forthe selected near-field earthquakes.

Keywords Shape memory alloy · Viscous fluid damper · Hybrid damper ·Near-field earthquakes · Passive energy dissipation devices

S. Roy (B) · P. SahaSchool of Civil Engineering, KIIT Deemed to be University, Bhubaneswar, Odisha, Indiae-mail: [email protected]

P. Sahae-mail: [email protected]

S. DasDepartment of Civil Engineering, C. V. Raman Global University, Bhubaneswar, Odisha, Indiae-mail: [email protected]

© Springer Nature Singapore Pte Ltd. 2021S. Adhikari et al. (eds.), Advances in Structural Technologies, Lecture Notesin Civil Engineering 81, https://doi.org/10.1007/978-981-15-5235-9_1

1

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2 S. Roy et al.

1 Introduction

In recent years the use of base isolators for seismic protection of structures hasattracted the interest of many researchers. During an earthquake, a finite quantityof energy in the form of vibration is stuck directly at the base of the structure, sothe technique of isolating the base has been adopted to preserve the stability of thestructure. The flexibility of the connection or dampers between the substructure tosuperstructure produces enough counter-response to the ground excitation remainingthe structure sustainable. The performance of the base isolation system depends uponthe capacity by which the system’s fundamental frequency can be shifted to a valuelower than that of the unmodified structure and its capacity to dissipate energy [1].

With the advancement in technologies, there is an increasingly important role ofpassive energy dissipation system for seismic protection of structures. The passivedampers when installed on a structure functions by absorbing a part of the inputseismic energy and hence, minimizing the amount of energy needed to be dissi-pated by the primary structural members, thus reducing possible structural damages.The passive dampers are mainly categorized into rate-independent devices and rate-dependent devices [2]. The mechanical response of rate-dependent devices dependson the relative velocity between the ends of the device. For example, viscoelasticfluid dampers (VFD) are rate dependent devices which have dynamic behavior char-acterized by their ability to lower stiffness values within a range of given frequen-cies and have a negligible influence on the fundamental natural frequency. ShapeMemory Alloys (SMA) dampers are rate-independent devices whose mechanicalresponses depend on displacement occurring between both the ends of the deviceand describes by nonlinear hysteretic models. SMAs exhibit several unique proper-ties such as recovery to original shape after large deformation due to the effect ofheating (shape memory effect) or due to the object being loaded (super-elasticity)[3]. Re-centering, high damping capacity, minimal maintenance, high fatigue resis-tance, and durability are the characteristics which make SMAs an effective dampingdevice or a base isolator [4, 5]. In case of SMA, a hysteretic cycle is obtained whichreduces the transmission of energy to the structure by the help of a hysteretic cycle,which dissipates energy within its own area [6].

In this study, a G+ 4 storey building has beenmodeled and the performance of thebuilding under near-field earthquakes taking into consideration the Tabas earthquake,Kobe earthquake, and Gebze earthquake. The present study aims to compare theperformance of isolation system when the individual dampers, VFD and SMA, andHybrid damper, combination of both VFD and SMA, are installed at the base of thestructure.

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Seismic Control and Performance of Passive Hybrid … 3

Table 1 Details of the near-fault earthquakes considered for study

Earthquake Distance (km) PGA (g) Magnitude Year

Tabas (Boshrooyeh station) 17 0.8 7.4 1978

Kobe (Kakogawa station) 22.5 0.8 6.9 1995

Gebze (Yarimca station) 22.7 0.3–0.4 7.4 1999

2 Near-Field Earthquakes

The earthquakes occurring on the earth’s surface close to the fault are referred to asnear-field earthquakes. The distance ranges from 10–60 km around the fault [6].These earthquakes have long-pulse periods and high accelerations. During faultrupture, a part of the wave is transferred to the site location, and if the site is inthe same direction, they get closer to each other, thus generating a large pulse whichdampens with time length during which waves gets to the structure. But in caseof the site being located in the opposite direction to that of the occurred fault, thedistance between the site and the waves increases incrementally, and hence longertime is required for the waves to reach the structure [7]. Due to this long period ofoscillation, which may sometimes be to close to the natural oscillation, the structuretends towards resonance condition. This condition causes more structural damagesand more fragile behavior of the structure. Table 1 below shows details of somenear-fault earthquakes considered in the present research study.

3 Shape Memory Alloy (SMA)

Seismic Isolation system using Shape Memory Alloy or SMA has attracted goodattention as a smart material and has been used effectively in passive protection ofstructures [8]. Shape memory effect and super-elasticity are two unique propertiesof SMA, in which the former refers to the property by which the SMA retains thepredefined shape and returns back to it when agitated and the latter refers to theproperty by which SMA undergoes large inelastic deformations and recovers its ownshape upon unloading [9]. The schematic diagram of an SMA damper is shown inFig. 1. When under excitation, the SMA dampers generate a controlled force whichmakes the main structure safe against earthquake. The schematic diagram of theworking of SMA damper is shown in Fig. 2. The SMA dampers follow the passivecontrol concept bywhich it absorbsmajor part of input energy due to seismic activity,or undergoes major damage, keeping the structural members in the elastic limit ormakes sure that the structure undergoes minimal damage.

No external power source is required for a passive control system and structuralcontrol using SMAs makes use of its damping property to reduce the structuralresponse and subsequent structural damage subject to severe vibration or loading [9].The hysteresis loop for the SMA Damper is shown in Fig. 3. The hysteresis loop for

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4 S. Roy et al.

(a) Cross Sectional View (b) Re-Centering Group

(c) Energy Dissipating Group

Fig. 1 Schematic detailed figure of SMA Damper showing (1) Internal Shaft, (2) Shim Plate, (3)Pre-Compressed Spring, (4) External Tube, (5) Middle Anchor, (6) Side Anchor, and (7) SMAwires [10]

Fig. 2 Schematic diagram of performance evaluation passive structure [10]

(a) Energy Dissipating Part (b) Re-Centering Part (c) SMA Damper

Fig. 3 Hysteresis loop for SMA Damper as presented using Bouc-Wen model [10]

energy dissipation and re-centering has been shown in Fig. 3a and b, respectively. Thecombination of the behavior of both these functional groups represents the hysteresisloop for SMA damper which is represented in Fig. 3c. Thus, the graph shows bothself-centering capability and maximum energy-dissipating capacity. As discussed,SMA damper, being highly nonlinear material, is difficult to model based on somefixed rules. However, the mathematical model for hysteresis loop of SMA damper iseffective for a damper control structure [10].

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Seismic Control and Performance of Passive Hybrid … 5

The energy dissipating device restoring force is shown as [11]:

Frestore = αK0x + (1− α)K0Zs (1)

where x is the displacement or the elastic part, α indicates the ratio between post-yielding to pre-yielding stiffness, K0 is the linear stiffness, and Zs is the hysteresispart of the isolator displacement. The maximum displacement in the austenite phaseis denoted by a and b, and is the displacement responsible for martensitic transforma-tion. In order to linearize the complex nonlinear equation of the hysteresis curve, alinearized equation is introduced which minimizes the residual error of the nonlinearand linear terms of governing equation of motion. The simplified linearized versionof Zs is given as Eq. 2 [12, 13]:

Zs =[1− sgn{sgn(|xs| − a) + 1}]xs+ {sgn(|xs| − a) + 1}

2

[ {sgn(xs) + sgn(xs)}2

(b − a) + a sgn(xs)

](2)

where sgn(xs) is signum function:

sgn(x) =⎧⎨

1 if xs > 00 if xs = 0−1 if xs < 0

4 Viscous Fluid Damper (VFD)

The implementation of Viscous fluid damper (VFD) has been recently adapted forseismic protection of buildings. A Viscous fluid damper comprises of piston withina damper housing which is filled with silicon oil acting as a fluid [2]. The pistonconsists of numerous small orifices through which the movement of fluid occursfrom one part of the piston to the other part. The schematic cross-sectional figure ofVFD is shown in Fig. 4. When the piston rod is stroked, the fluid is pressurized toflow through the orifices. This creates a pressure differential across the piston headwhich produces very large forces, thus resisting the relative motion of the damper[14, 15]. The fluid flows at a higher velocity thus resulting in the generation offriction force between fluid particles and piston head. This force is responsible forenergy dissipation in the form of heat. This damping force reduces both stress anddisplacement in the structure. In a viscous fluid damper, the resistive control forceis:

f = Cd|xb| λsgn(xb) (3)

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6 S. Roy et al.

Fig. 4 Schematic cross-sectional figure of VFD [14]

Fig. 5 Force Displacementrelation in case of VFD [14]

In the above equation, f indicates damping force,Cd indicates damping coefficientwith units of force per velocity, xb indicates velocity across both the ends of damper,λ indicates velocity exponent whose value ranges between 0.4 and 1.4. The force–displacement relation of VFD is shown in Fig. 5. The performance of passive VFDdepends upon its velocity exponent (λ) and damping coefficient (Cd).

5 Numerical Study

A G + 4 model R.C.C. framed structure was analyzed using MATLAB [16] forthe three earthquakes to study the performance of the hybrid control system. Thebuilding is a 3 * 3 bay-framed structure with a ground-level height of 5.2 m, storeyheight of 3.1 m, and bay distance of 5 m as shown in Fig. 6. The time history analysisis performed using the State Space Method on the equations of motion in order toobtain the structural response of the building [17].

The equation of motion for SDOF system may be written as (Eq. 4) [18, 19]

MX(t) + CX(t) + KX(t) = −MUg + FE(t) (4)

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Seismic Control and Performance of Passive Hybrid … 7

a) Elevation

b) Plan

Fig. 6 The Basic Structural Frame of G + 4 building (a) Elevation and (b) Plan

where, FE(t) the external force, M indicates the mass matrix, C indicates thedamping ratio matrix, K indicates the stiffness matrix, Ug is ground acceleration,X(t), X(t), and X(t) are displacement, velocity, and acceleration, respectively.

State Space Equation has been employed for smart base isolation structuralproblem and is given by Eq. 5.

x(t) = Ax(t) + Bu(t) + EUg(t) (5)

where u(t)= f d(t) is the time-varying control device force, x consists of the states,and A, B, and E are the system matrices defined as

A =[

0 I−M−1K −M−1C

], B =

[0

M−1�

], E = −

[0�

]

whereΛ and Γ are the location of the device and the earthquake influence vector,respectively.

Timehistory analysis is performedusingnear-field earthquakes taking into consid-eration the three earthquake ground motions namely Tabas (1978), Kobe (1995),and Gebze (1999) earthquake to obtain the uncontrolled and controlled structuralresponses of the building. The time history of the earthquakes for a time period of60 s is shown in Fig. 7. Passive damper SMA and VFD and Hybrid are installedat the base of the structure. The effectiveness of the Hybrid Damper is investigatedagainst individual dampers. Time history analysis is performed for the uncontrolledand controlled responses under the earthquakes. The lumped masses (mi), storeystiffness (ki), and damping ratio (ξ i) for every storey of the superstructure have beenconsidered identical for the sake of simplicity. The mass ratio (ξ ) (i.e., ratio betweenisolator mass to the total superstructure-isolation system mass) is taken as 2% and

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8 S. Roy et al.

-100

-50

0

50

100

0 10 20 30 40 50 60

Acce

lera

tion

(cm

/s2 )

Time(s)

Tabas (1978)

-10

-5

0

5

10

0 10 20 30 40 50 60

Acce

lera

tion

(cm

/s2 )

Time(s)

Kobe (1995)

-400-300-200-100

0100200

0 10 20 30 40 50 60

Acce

lera

tion

(cm

/s2 )

Time (s)

Gebze (1999)

Fig. 7 Time History of Tabas (1978), Kobe (1995), Gebze (1999), respectively

the structural time period (T ) is 0.55 s. The superstructure damping (ξ b) assumedis of viscous type and taken as 5% [9]. αs is the constant determining the ratio ofpre-transformation to post transformation stiffness caused during the load deforma-tion behavior of SMA which has been considered as 0.1. Maximum displacementin the austenite phase is represented by a and b and is the displacement responsiblefor martensitic transform which has been obtained from experiments conducted byShinozuka et al. [12], and has been taken as 0.005 and 0.05, respectively. The timeperiod (T b) for the damper was taken as 2 s. The value of Cd considered for VFDdamper is 1500. The parameters considered for the SMA damper force–deformationhysteresis loop has been shown in Table 2 [20].

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Seismic Control and Performance of Passive Hybrid … 9

Table 2 Structuralparameters and SMAparameters considered fordesign

Structural parameters SMA parameters

T = 0.55 s Tb = 2 s

ξ = 2% ξb = 5%

αs = 0.10

a = 0.005

b = 0.05

6 Results and Discussions

The time history analysis has been performed in order to calculate the structuralresponses of the structure for the three specified near-field earthquake groundmotions. The three specified near-field earthquakes are: (1) 1978 Tabas (Boshrooyehstation) with PGA (peak ground acceleration) equals to 0.8 g having a hypocentraldistance of 17 km; (2) 1995 Kobe (Kakogawa station) with PGA value equals to0.8 g and hypocentral distance 22.5 km; (3) 1999 Gebze (Yarimca station) with PGAvalue equals to 0.3–0.4 and the hypocentral distance of 22.7 km.

From the earthquake data, a comparison has been carried out between base shearand displacement for uncontrolled structure and structure fitted with dampers. Thetime variation of the displacement response of the earthquakes for a damping ratio of1.5% for VFD and 2% for SMA and Hybrid damper combination of SMA and VFDare shown in Fig. 8. In this figure, the displacement response of the structure has beencompared for both uncontrolled structure and structure individually incorporatedwith SMA, VFD, and next by Hybrid of SMA and VFD. From the figures, it can beobserved that when the model was applied to the Tabas earthquake, the reductionin displacement by Hybrid damper is 4% more than that of VFD and 8% morethan that of SMA. Then in case of Kobe earthquake acceleration, the reduced valueof displacement by Hybrid damper is about 2% and 7% more than that of VFDand SMA. While considering the Gebze earthquake acceleration data, the Hybriddamper reduces displacement by about 4% more than of VFD and 7% more than ofSMA. Thus, the control system has helped to reduce the structural displacement thuspreventing damage to the structure.

The base shear of the structure has been compared for the uncontrolled and SMA,VFD, andHybrid damper incorporated structure and shown in Fig. 9. From the figure,it can be observed that the model when incorporated with a Hybrid damper underTabas earthquakemotion data reduces the base shear response by 11%more than thatofVFD and 16%more than that of SMA. In case ofKobe earthquake acceleration, theHybrid damper reduces the base shear responses by about 10% and 13% more thanthat of VFD and SMA. Further, under Gebze earthquake motion the Hybrid damperis effective in reducing the base shear response by 4% more than VFD and 7% morethan SMA. Thus, the hybrid damper is successful in absorbing the input seismicenergy and dissipating the samemore effectively thanVFDand SMA, thus protectingthe main structure from damage. As a whole, considering all the three earthquake

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10 S. Roy et al.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0

Disp

lace

men

t(m

)

-0.2

-0.1

0

0.1

0.2

0

Disp

lace

men

t(m

)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0

Disp

lace

men

t (m

)

10

U

10

U

10

Uncon

20

ncontrolled

20

ncontrolled

20

ntrolled

30

Time(s)

VFD

30

Time(s)

VFD

30

Time (s)

VFD

40

SMA

40

SMA

40

SMA

50

Hybrid

50

Hybrid

50

Hybr

60

(a)

60

(b)

60

rid

(c)

Fig. 8 Uncontrolled and displacement controlled by the dampers for a Tabas (1978), b Kobe(1995), c Gebze Earthquake (1999)

motions, we can say that maximum reduction in displacement and base shear usingHybrid damper is obtained as 8% and 16%, respectively, when compared to VFD andSMA. With the application of Hybrid damper both the displacement and base shearhas been controlled and the damage to the structure due to long duration, near-fieldearthquakes can be prevented. Thus, the structural responses of the structure havebeen reduced, hence proving the effectiveness of the Hybrid damper.

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Seismic Control and Performance of Passive Hybrid … 11

-150

-100

-50

0

50

100

150

0Base

She

ar(k

N)

-150

-100

-50

0

50

100

150

0Base

She

ar (k

N)

-40

-20

0

20

40

0

Base

She

ar (k

N)

10

U

10

Unc

10

Uncontr

20

ncontrolled

20

controlled

20

rolled

30

Time(s)

VFD

30

Time(s)

VFD

30

Time (s)

VFD

40

SMA

40

SMA

40

SMA

50

Hybrid

50

Hybrid

50

Hybrid

60

(a)

60

(b)

60

(c)

Fig. 9 Uncontrolled and controlled base shear responses by the dampers for a Tabas (1978), bKobe(1995), c Gebze Earthquake (1999)

7 Conclusion

In this paper, a G+ 4 building has been modeled and an attempt is made to comparethe effectiveness of Hybrid damper which comprises of VFD and SMA combined.The performance of the building is under three near-field earthquakes, Tabas, Kobe,and Gebze are investigated. Based on the investigation, the performance of Hybriddamper is found to be better than the performance of individual VFD and SMA, inregard to seismic response control of the building. The hybrid damper is found tobe robust as it works on the combined principle of energy dissipation property from

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12 S. Roy et al.

VFD and re-centering ability from SMA. The following conclusions are drawn fromthe research paper:

1. Generally, the near-field earthquake causes higher structural damage but with theapplication of a Hybrid damper, the G + 4 structure was seismically controlled,hence showing good dampening performance and damage reduction.

2. Higher reduction in seismic response of building can be obtained by the instal-lation of a Hybrid damper in the base of the building than that of VFD and SMAinstalled individually at the base.

3. Reduction in seismic response displacement of the building usingHybridDamperis obtained as about 4% more than that of VFD alone and 8% more than that ofSMA alone.

4. The reduction in the shear response of base using hybrid damper has beenobserved to be about 11% more than that of VFD and 16% more than that ofSMA for all the three earthquakes, hence showing that hybrid damper is betterin mitigating floor displacement and base shear.

References

1. Ibrahim RA (2008) Recent advances in nonlinear passive vibration isolators. J Sound Vib314:371–452

2. Castaldo P (2014) Passive energy dissipation devices. In: Integrated seismic design of structureand control systems. Springer, Switzerland, pp 21–62

3. Sepulveda J,BoroschekR,HerraraR (2008)Steel beam-columnconnection using copper-basedshape memory alloy dampers. J Constr Steel Res 64:429–435

4. Motahari SA, Ghassemieh M, Abolmaali SA (2007) Implementation of shape memory alloysdampers for passive control of structures subjected to seismic excitations. J Constr Steel Res63:1570–1579

5. Des Roches R, Mc Cormick J, Delemont MA (2004) Cyclical properties of superelastic shapememory alloys. ASCE J Struct Eng 130(1):38–46

6. Heydari M, Mousavi M. The comparison of seismic effects of near-field and far-field earth-quakes on relative displacement of seven-storey concrete building with shear wall. Int Res JEnviron Sci (Iran)

7. Taheri JS, Anderson JG (1988) The 1978 Tabas, Iran earthquake: An interpretation of the strongmotion records. Bull Seismol Soc Am 78(1):142–171

8. Ozbulut E, Hurlebaus S (2010) Evaluation of the performance of a sliding-type base isolationsystem with a NiTi shape memory alloy device considering temperature effects. Eng Struct32:238–249

9. Song G, Li HN (2006) Applications of shape memory alloys in civil structures. Eng Struct28:1266–1274

10. Ma H, Yam MCH (2011) Modelling of a self-centring damper and its application in structuralcontrol. J Constr Steel Res 67: 656–666 (Elsevier)

11. Ikhouane F, Rodellar J (ed) (2007) Systems with hysteresis: analysis, identification and controlusing the Bouc–Wen model. Wiley, Chichester (England, Hoboken, NJ)

12. Shinozuka M, Chaudhuri SR, Mishra SM (2015) Shape-Memory-Alloy supplemented LeadRubber Bearing (SMA-LRB) for seismic isolation. J Sound Vib 41:34–45

13. Yan X, Nie J (2000) Response of SMA super elastic systems under random excitation. J SoundVib 238(5):893–901

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Seismic Control and Performance of Passive Hybrid … 13

14. Kumar PS, Naidu MV, Mohan SM, Reddy SS (2016) Application of fluid viscous dampers inmulti-story buildings. Int J Innov Res Sci Eng Technol 5(9):17064–17069

15. Marko J, Thambiratnam D, Perera N (2006) Study of viscoelastic and friction damperconfigurations in the seismic mitigation of medium-rise structures. J Mech Mater Struct1(6):1001–1039

16. MATLAB. The Math Works Inc. Natick Massachusetts (2010)17. Saha P, Jangid RS (2009) Seismic control of benchmark cable stayed bridge using passive

hybrid systems. IES J Part A Civ Struct Eng 2(1):1–1618. Chopra AK. Dynamics of structures—theory and applications to earthquake engineering.

Prentice Hall19. Elnashai AS, Sarno LD (2008) Fundamentals of earthquake engineering. Wiley20. RoyS,DasS, SahaP (2018) Seismic response control of a building using passive hybrid damper.

In: Structural engineering convention-2018. Jadavpur University Press, Jadavpur University,Kolkata

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Wall Effects on Terminal Velocity of TestFuel Bundle in the Fuel Test Loopof High Flux Research Reactor

G. Verma, S. Sengupta, S. Mammen, P. Mukherjee, and P. V. Varde

Abstract Fuel Test Loop (FTL) is a self-contained independent experimental loopwhich is designed for testing of nuclear fuel materials under simulated power reactorconditions in the High Flux Research Reactor being developed at BARC. It is ahigh-pressure loop with maximum operating pressure up to 17.5 MPa and maximumoperating temperature up to 330 °C. The In-Pool Test Section of the FTL consistsof a series of concentric tubes with different thicknesses and functionality. The testfuel bundle resides within the innermost Fuel Tube which is further enclosed withinan internally insulated Pressure Tube which acts as a pressure boundary enclosureto the test fuel bundles. The present work deals with the investigation of wall effectson the terminal velocity of test fuel bundles falling under gravity within the In-PoolTest Section. While loading/unloading of the test fuel bundle, accidentally the fuelbundle may fall under the influence of gravity within the fluid filled Fuel Tube.The minimum gap between the fuel bundle and the fuel tube is 2 mm. Thus, thewall effects on the velocity of the falling fuel cannot be neglected. The purposeof the present work is to estimate this wall effects on the terminal velocity of thefalling fuel in terms of Drag Coefficient. This involves, initially estimating dragcharacteristics and terminal velocities with wall effects for different geometries, andfinally predicting the overall characteristics with the test fuel bundle as the geometry

G. Verma (B) · S. Sengupta · S. Mammen · P. MukherjeeResearch Reactor Design and Projects Division, Bhabha Atomic Research Centre, Mumbai400085, Indiae-mail: [email protected]

S. Senguptae-mail: [email protected]

S. Mammene-mail: [email protected]

P. Mukherjeee-mail: [email protected]

P. V. VardeResearch Reactor Services Division, Bhabha Atomic Research Centre, Mumbai 400085, Indiae-mail: [email protected]

© Springer Nature Singapore Pte Ltd. 2021S. Adhikari et al. (eds.), Advances in Structural Technologies, Lecture Notesin Civil Engineering 81, https://doi.org/10.1007/978-981-15-5235-9_2

15

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16 G. Verma et al.

of interest. To fulfill this objective, an analytical methodology is established whichhas been validated through a commercial code.

Keywords Terminal velocity · Test fuel bundle · Wall effect · Drag coefficient

Nomenclature

CD Drag coefficientRe Reynolds Numberf Velocity ratio or wall factorUt Terminal velocity in confined mediumUt∞ Terminal velocity in infinite mediumdp Diameter of sphereρp Density of sphereD Fall Tube Diameterρ f Fluid Densityμ Fluid Viscosityλ Sphere-to-tube diameterds Diameter of sphere with volume equal to that of nonspherical particleL Length of the CylinderV Volume of the objectdA Projected Area DiameterAp Projected Areak Volumetric Shape Factorϕ SphericityAv Surface area of a sphere having the same volume as of the particlemp Mass of the particleg Gravitational accelerationdc Cylinder diameterGa Galileo NumberGa′ Modified Galileo NumberE Aspect ratio of the nonspherical particleReT Reynolds Number in the Newtonian RegimeReL Reynolds Number in the Stokes and Transitional flow regimeT 1, T 2 Weighting Factor

1 Introduction

The FTL in the proposed High Flux Research Reactor (HFRR) is a high-temperatureand high-pressure experimental loop to perform testing of nuclear fuel of powerreactors under similar conditions. The maximum operating pressure and temperature

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Wall Effects on Terminal Velocity of Test Fuel … 17

of the FTL is 17.5 MPa and 330 °C, respectively. The FTL consists of two sections,the In-Pool Test Section and Out-of-Pool Section. The In-Pool test section providesa pressure boundary enclosure to the test fuel bundles and also a separation betweentest section high-temperature/pressure water with the pool water. It is designed suchthat it maintains its mechanical strength and structural integrity over the lifetime ofthe reactor. The Out-of-Pool section consists of various process systems (such asMain Loop System, Purification and Sampling System, Pressurizer System, JacketCoolant System, etc.), piping, and equipment necessary to maintain the requiredtemperature, pressure, and flow conditions inside the In-Pool test section.

The In-Pool Test Section of the FTL consists of a series encapsulation of fourconcentric tubes (Fuel Tube, Pressure Tube, Inner Jacket Tube, and Outer JacketTube) with different thickness and functionality. The present work investigates walleffects on the terminal velocity of test fuel bundles accidentally falling under gravitywithin the 4.5 m long fuel tube of the In-Pool Test Section while loading/unloadingof the test fuel bundle. Since minimum gap between the falling fuel bundle andthe fuel tube is very small, the wall effects on the falling fuel velocity need to beestablished. The present work estimates this wall effects on the terminal velocityof the falling fuel in terms of Drag Coefficient. For this, drag characteristics andterminal velocities with wall effects for different geometries are estimated which isfurther utilized to estimate these characteristics for the geometry of interest using anestablished analytical methodology which is subsequently validated with fluid–solidinteraction coupled techniques through a commercial code (ESI CFD-ACE+).

2 Analytical Methodology

According to Gabitto and Tsouris [1], an object falling in an infinite fluid mediumunder the influence of gravity will accelerate until the gravitational force is exactlybalanced by the resistance force that includes buoyancy and drag. This constantvelocity, hence achieved is termed as “terminal velocity”. Corelations are developedby various researchers (Clift et al. [2], Kahn and Richardson [3], and Haider [4]) thatrelates drag coefficient (CD) and the Reynolds Number (Re) for objects of sphericalshape falling at their terminal velocities in an infinite medium. Further, there havebeen literature suggesting the retarding effects of the nearbywall on an object settlingin a liquid. Most of these investigations have involved a single sphere settling incylindrical/triangular/rectangular ducts in eitherNewtonian orNon-Newtonian fluids[5–7]. However, not much literature is available for complex geometries falling in aconfined flow passage under the influence of gravity.

To introduce the wall effects on the motion of a sphere falling axially in a cylin-drical tube filled with a stagnant fluid, as per Arsenijevic et al. [8], velocity ratio (f )or the wall factor is defined as

f = Ut

Ut∞= (

1 − 1.12λ1.26)0.7

(1)

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18 G. Verma et al.

where Ut is the terminal velocity of the falling sphere (diameter dp and density ρp)settling along the axis of a tube of diameter,D, in a fluid medium of density (ρ f ) andviscosity (μ), whereasUt∞ denotes the unbounded velocity of the same sphere in thesame liquid in the absence of walls.λ denote the ratio of the sphere-to-tube diameter(dp

/D). Other widely used correlations in the turbulent flow regime are those of

Newton [9], as shown in Eq. (2) and of De Felice [10], as presented in Eq. (3).

f = (1 − λ2

)(1 − 0.5λ2

)0.50.11 ≤ λ ≤ 0.83 (2)

f =(

1 − λ

1 − 0.33λ

)0.85

(3)

For nonspherical particles (such as cylinders), Chhabra [11], correlated the wallfactor as

f = 1 − 1.33(ds/D) (L/D) < 10 (4)

f = 1 − 3.58(ds/D) (L/D) > 10 (5)

where ds is the diameter of a sphere with volume equal to that of a nonsphericalparticle and D is the fall tube diameter through which the cylinder is falling. Thelength of the cylinder is taken as L.

In order to calculate the terminal velocity of the cylindrical object, various empir-ical relations have been proposed. One such factor is the “volumetric shape factor”defined by Heywood [12] as

k = V

d3A

(6)

where, V is the volume of the object and dA = (4Ap/π

)0.5is the projected area

diameter, which is calculated as the diameter of a sphere with the equal projectedarea as that of the particle, and Ap is the projected area of the object.

The degree of sphericity is given by Wadell [13] as

φ = AV

A(7)

whereAV is the surface area of a sphere having the same volume as that of the particle,and A is the actual surface area of the particle. The sphericity of a true sphere is equalto 1.